[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207761-en":3,"doc-seo-207761-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207761,962084928904,"Jake","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","GCSE Maths - Ratio, Proportion and Rates of Change - Compound Growth and Decay Worksheet","GCSE Maths worksheet focused on compound growth and compound decay under ratio and proportion learning objectives. It provides worked and guided examples using percentage change to model populations, depreciation, leakage and depreciation of assets, and bank interest with compounding. Section A applies percentage increase to find future quantities after multiple years, while Section B applies percentage decrease to calculate remaining amounts. Section C consolidates compound interest and additional interest earned or paid on loans and deposits.","# GCSE Maths – Ratio, Proportion andRates of Change\n\nCompound Growth and Decay  \nWorksheet  \n## NOTES\n\nSOLUTIONS  \nThis worksheet will show you how to work out different types of compoundgrowth and decay questions. Each section contains a worked example, aquestion with hints and then questions for you to work through on your own.  \n## Section A\n\nWorked Example  \nThe population of 250 rabbits in a field increases by 3% each year. How manyrabbits will there be after 4 years?  \nStep 1: Find values for 􀜰0 and 􀝐 for use in the formula 􀜰 = 􀜰0 × 􁉀 1 + 􀯡 .  \n􀜰0 = 250  \n􀝐 = 4  \nStep 2: Substitute into the formula to calculate the value of N.  \n􀜰 = 􀜰0 × 􀵬 1 + 􀯡  \n􀜰 = 250 × 􀵬 1 + 4  \n􀜰 = 250 × 1.034 = 281.377 …  \nStep 3: Form a conclusion.  \nTo the nearest whole number there will be 281 rabbits in the field after 4 years.  \n## Guided Example\n\nThe population of a beehive is currently 2000, however due to some circumstancesthe population is increasing by 7% a year. What is the population of the beehiveafter 10 years to 3 significant figures?  \nStep 1: Find values for 􀜰0 and 􀝐 for use in the formula 􀜰 = 􀜰0 × 􁉀 1 + 􀯡 .  \nStep 2: Substitute into the formula to calculate the value of N.  \nStep 3: Form a conclusion.  \nNow it’s your turn!  \nIf you get stuck, look back at the worked and guided examples.  \n1. Red Squirrels are entering the UK at a rate of 5.2% a year. Currently there are 590red squirrels in the UK. What is the expected number red squirrels after 6 years?  \n2. UK retirees are migrating to holiday homes in Spain. Every year, 2.3% of UKresidents move to Spain. In 2021, there are 2700 UK retirees. How many retirees willthere be in 2027?  \n3. On Tuesday 30,000 people tested positive for Covid-19. The health secretaryestimates the cases increases 4.7% a day. How many more people have testpositive on Sunday than Tuesday?  \n4. In 2010, the population of trout in a fishery is 4000. In 2016, the new population is  \n5642. What is the population growth rate?  \n## Section B\n\nWorked Example  \nThe population of 10,000 rabbits in a field decreases by 10% each year due to foodshortages. How many rabbits will there be after 4 years?  \nStep 1: Find values for 􀜰0 and 􀝐 for use in the formula 􀜰 = 􀜰0 × 􁉀 1 − 􀯡 .  \n􀜰0 = 10,000  \n􀝐 = 4  \nStep 2: Substitute into the formula to calculate the value of N  \n􀜰 = 􀜰0 × 􀵬 1 − 􀯡  \n􀜰 = 10,000 × 􀵬 1 − 4  \n􀜰 = 10,000 × 0.94 = 6561  \nStep 3: Form a conclusion.  \nThere will be 6561 rabbits in the field after 4 years.  \n## Guided Example\n\nThe value of a gold necklace is depreciating at a rate of 0.04% a year. Currently it isworth £13,000 . What will the value be after 7 years?  \nStep 1: Find values for 􀜰0 and 􀝐 for use in the formula 􀜰 = 􀜰0 × 􁉀 1 − 􀯡 .  \nStep 2: Substitute into the equation to calculate the value of N.  \nStep 3: Form a conclusion.  \nNow it’s your turn!  \nIf you get stuck, look back at the worked and guided examples.  \n5. Water in a tank is leaking at a rate of 5.5% a second. The tank is filled up with 6 􀝈 ofwater. How much water is left after 8 seconds? Give your answer in millilitres.  \n6. A new car is bought for £15,000 . It depreciates by 33% each year. Tim sells his carfor the value after 3 years. How much did Tim lose?  \n7. A bouncy ball is thrown from a height of 5 m. It bounces at a height 4.5% less thanthe height before. How many bounces does it take for the ball to be under 1 m ofheight?  \n8. The value of a car depreciates at the rate 􀝔 % . In 2020, the value is £21,000 . In 2028,the value of the car is approximately £11,255 . Find the value of 􀝔 .  \n## Section C\n\nWorked Example  \nHana deposits £800 in a bank that pays 4.5% compound interest a year. Work outthe interest paid by the bank in 3 years.  \nStep 1: Find values for 􀜰0 and 􀝐 for use in the formula 􀜰 = 􀜰0 × 􁉀 1 + 􀯡 .  \n􀜰0 = 800  \n􀝐 = 3  \nStep 2: Substitute into the formula to calculate the value of N.  \n􀜰 = 􀜰0 × 􀵬 1 − 􀯡  \n􀜰 = 800 × 􀵬 1 +  3  \n􀜰 = 800 × 1.0453 = 912.9329  \nStep 3: Calculate how much interest this is.  \n􀜫􀝊􀝐􀝁􀝎􀝁􀝏􀝐 􀜲􀜽􀝅􀝀 = 􀜰􀝁􀝓","cbCaifU7s5s9frcq","https://ap.wps.com/l/cbCaifU7s5s9frcq","pdf",330122,1,10,"English","en",105,"# NOTES\n# Section A\n## Worked Example\n## Guided Example\n# Section B\n## Worked Example\n## Guided Example\n# Section C\n## Worked Example\n## Guided Example","[{\"question\":\"How do you calculate compound growth over several years on this worksheet?\",\"answer\":\"Use the compound growth form N = P0 × (1 + r)^t, substitute the starting value, rate and time, then round to the nearest whole number when asked.\"},{\"question\":\"What formula is used for compound decay questions in Section B?\",\"answer\":\"Use N = P0 × (1 − r)^t for a percentage decrease each period, then substitute and evaluate to find the remaining amount.\"},{\"question\":\"How are compound interest and loan interest questions handled in Section C?\",\"answer\":\"Compute the future value using P0 × (1 + r)^t, then subtract the original deposit/loan to find the interest paid or earned, with results given in pounds to appropriate precision.\"}]","GCSE Maths - 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